Manuscript Oai280-C@1 · Oai280-C.tex · proposition · 7d44b8c0

Proposition: Uniform decoder-class obstruction

Finite-confidence certification › Simultaneous decisions · lines 1643–1666 · proof included or linked

Oai280-C@1#prop:optimal

Let $D_{A}$ be a declared decoder class for the actual accessible channel, and define

e_{A}^{opt} = D \in D_{A} in f d_{⋄} (D N_{A}, T_{A}) .

If a separately proved bound is uniform over the class, $e_{A}^{opt} \geq g_{A}$ , then $g_{A} > ε_{A}$ excludes every allowed decoder. A certified candidate $D \in D_{A}$ with upper bound $U_{D}$ gives

g_{A} \leq e_{A}^{opt} \leq U_{D}

on the coverage event. A lower bound for one tested decoder does not provide a lower bound for $e_{A}^{opt}$ .

Proof. The first statement is the definition of a uniform lower bound. The second follows by evaluating the infimum at the candidate.

Displayed formulas in this passage

unlabeled · line 1647
$e_{A}^{opt} = D \in D_{A} in f d_{⋄} (D N_{A}, T_{A}) .$
unlabeled · line 1655
$g_{A} \leq e_{A}^{opt} \leq U_{D}$

Proposition: Uniform decoder-class obstruction

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